The answer is not a straight yes or no.
It all depends on the current being drawn by the circuit versus the turn on current needed to have a stable zener voltage.
I had to download the SX-525 service manual from Hifi engine to look at the circuit, since I have not worked on an SX-525 before.
I could only find the 32/33v zener right off, I couldn’t find the 12v one in AWR-007.
Still for the 33v zener the circuit (of AWR-007) shows a voltage of 41.5v at one end of R2 (the current limiting resistor for the zener), with the other side at 32.5v. That gives a voltage drop across R2 of 9 volts.
So the current through R2 is I=V/R or I=9v/1500 ohms = 6mA.
So that zener is drawing 6mA across 32.5v for a power handling of P= V*I or P=0.006*32.5v = 195 mW.
I have neglected the current through R3 into the base of Q1 to make it easy.
Q1, the NPN is likely to have a high gain, at least 100, if I assume that, the base current will be only a fraction of 1 mA (with out going deeper into the circuit analysis) think it is safe to ignore.
If you want be safer you can use 6-1=5 mA for the zener power calculation. That would give you
P=0.005*32.5= 163mW (instead of 195mW).
So you see the zener is running on the higher side of its rating but still within the 250mWs.
Oooops.
Added this edit.
The zener is a 500mW zener not 250mW, as I stated above.
So it is running well with in its range. (Peter)
As to the yes or no on using the 1 Watt zener, if the data sheet on a new 1 watt zener shows it will be well turned on with 5 mA flowing through it then you are safe in using it.
My guess is that most if not all 1 Watt zeners will be ok for this circuit.
But you really need to know the current the circuit will be pulling through the zener first to be sure.
So that means you have to do some math to be sure.
It is not a straight forward yes or no, more like probably ok, but if you don’t check it could be a bad assumption.
I hope I have not caused your eyes to cross with all the math and calculations.